Sijia NI (倪思佳), Yixi CAI (蔡忆昔), Yunxi SHI (施蕴曦), Weikai WANG (王为凯), Nan ZHAO (赵楠) and Yirui LU (卢奕睿)

School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang 212013, People’s Republic of China

Abstract Packed-bed reactors (PBRs) hold great promise for environmental applications, but a deeper understanding of the behavior of plasma discharge within PBRs is required.To this end, a partial-discharge alternative equivalent circuit for PBRs was established in this work.Dielectric particles (glass beads or glass sand) were used to place focus on the effects of the particle size and shape on the partial discharge behavior of the oxygen PBRs.Some electrical characterizations were explored (e.g.the effective dielectric capacitance, partial discharge coefficient, and corrected burning voltage) that may differ from long-standing interpretations.The findings indicate that the suppressive effect of surface discharge on filament discharge is stronger with the decrease of the particle size.For partial discharge, the effective dielectric capacitance is always less than the dielectric capacitance.The corrected burning voltage and partial discharge tendency increase with the decrease of the particle size.As compared to an empty reactor,the average electric field in the PBR was found to be improved by 3-4 times,and the ozone energy efficiency and production were promoted by more than 20% and 15%,respectively.The plasma processing capacity can therefore be improved by choosing a relatively large size or a complex,irregularly-shaped packing material that is suitable for the discharge gap.

Keywords:packed-bed reactor,alternative equivalent circuit,partial discharge,packing particles,ozone

1.Introduction

Dielectric barrier discharge (DBD) is a widely-used method for the generation of non-thermal plasma [1-3].Of the various DBD reactors,packed-bed reactors(PBRs)have flexible options for packing materials to remove pollutants(e.g.NOX,CO2,PM)or improve ozone synthesis[4-8].Rayet altested the conversion of CO2into CO by packing (glass beads,Al2O3,TiO2,CeO2),and CeO2was found to result in the best conversion efficiency [9].Pekárek used TiO2particles to increase the ozone production yield of DBD in air[10].Many studies have reported that PBRs can improve energy efficiency, yet their behavior is poorly understood.The material properties, including the capacitance, dielectric constant, and shape factor, can affect the discharge phenomena within the packed bed [4-12].As PBRs are highly complex systems with many parameters, the optical techniques that are commonly used in other DBD systems are difficult to diagnose PBRs.Although experimental work and modeling in[13,14]have helped to progress the understanding of the discharge phenomena of these reactors, much research remains to be conducted.

Figure 1.Schematic diagram of the experimental setup.

In a general DBD system, Lissajous figures can be used to determine the electrical characterization without extensive calculations.To interpretQ-Vdata, the simplest equivalent circuit of DBD is commonly established, which can describe the switching of different load phases in a discharge cycle and reveal the basic relationship with load capacitance [15].However, the insertion of dielectric particles similar to electronic components into reactors can induce substantial changes in the equivalent circuit and affect the overall performance.Meiet alproposed a simple model, in which each independent particle is concentrated into a plate capacitor (Cpacking) connected to the capacitor of the gas (Cgas) in series [12]; this provides an effective way to understand the plasma discharge behavior in PBRs.Cpackingcan also be related to Lissajous figures by establishing an equivalent circuit.Peeters and Van proposed an alternative equivalent circuit of partial DBD that can thoroughly explain the phenomenon of the development of local discharge zones resulting in varied load capacitance [16]; it compensates for the insufficient explanation of the simplest circuit regarding this phenomenon [17].In PBRs, the situation of ‘not fully bridged-gap’ only exists when micro-discharge occurs in some voids, which is called partial discharge [18].The situation of fully-bridged-gaps tends to happen via the use of very high applied voltages [17], but this is not conducive to the service life of the reactors due to the influences of dielectric aging and thermal breakdown [19].Therefore, while understanding the behavior of PBRs during partial discharge can help expand their industrial applications, there exist few related reports.

In this study, a coaxial round tube, oil-cooled PBR was designed, and dielectric particles (glass beads or glass sand),instead of catalytic materials, were used as packing materials to avoid the influence of catalysis.The partial discharge behavior of the PBR was investigated, and the effects of the size and shape of packing particles were studied by establishing a partial-discharge alternative equivalent circuit for PBRs.The performance of the oxygen PBR in ozone synthesis was also analyzed to provide technical support for the broadening of their practical applications.

2.Experimental method and theory

2.1.Experimental setup

Figure 2.Structure of the PBR.

As shown in figure 1, the reactor was supplied by a highvoltage (HV) AC power supply (CTP-2000 K, Suman Electronics Co.,Nanjing,China)with a peak working voltage of 25 kV, adjustable from 7 to 20 kHz.A capacitor voltage divider consisted of 47 pF (C1) and 47 nF (C2) capacitors in series.Then the applied voltage signal was measured by an HV probe(P2220),and the current was recorded by a current probe(P6022).The voltage across the monitor capacitor(Cm)was measured by a probe(P6200),and electrical signals were sampled by an oscilloscope (TDS3034C).The discharge frequency was 7.5 kHz.Oxygen was used as the feed gas,and the flow rate was fixed at 5.0 l·min−1.The ozone concentration was measured by an ozone monitor(Interscan4480).

Figure 2 illustrates the structure of the PBR.A stainlesssteel tube with an external diameter of 40.0 mm and a wall thickness of 3.0 mm was placed in the center of a quartz tube as an HV electrode.The inner diameter of the quartz tube was 44.0 mm,the wall thickness was 3.0 mm,and a discharge gap of 2.0 mm was formed.The outer surface of the quartz tube was covered by a stainless-steel mesh fixed by copper wire and connected to the ground.A heat-dissipating insulating oil(Sinopec45#)was adopted for the reactor to cool the HV and ground electrode, and the circulation flow rate was fixed at 12.0 l·min−1.The cooling oil temperature was registered with thermocouples, and the temperature range was controlled within 18.0 °C-22.0 °C.

2.2.Evaluation of electrical parameters

To facilitate description, the capacitance involved in the reactor is marked, whileC1,C2andCmbelong to the measurement circuit,which are not added to figure 3.Figure 3(a)presents the simplest representation of an equivalent circuit for PBRs.Unlike the standard simplest equivalent circuit commonly used for DBD,Cpackingis added to this circuit.When PBRs discharge,only the gas gap is broken down,and the capacitances of the particles and the quartz tube still exist.Therefore,the dielectric capacitanceCdielof the PBR is equal to the series value of the quartz tube capacitanceCqzand the packing particle capacitanceCpacking.If the discharge gap is empty,Cpackingcan be regarded as a short circuit,andCdielis directly equal toCqz.Then,when the PBRs discharge off,theCcellcan be considered to comprise the gas gap capacitanceCgasand the dielectric capacitanceCdiel, as shown in figure 3(a).However, the simplest equivalent circuit for a PBR is theoretically applicable only when the gas gap is fully bridged,i.e.when theCgasis completely broken down.If the gas gap is not fully bridged, the reactor can be described as partial discharge.For a partial discharge DBD, an alternative equivalent circuit is required to accurately reflect the discharge behavior [16].After the addition ofCpacking, a partialdischarge alternative equivalent circuit for PBRs is established for the first time,as shown in figure 3(b).This electrical circuit is split into discharge and non-discharge sections by two coefficients α and β, and α + β = 1 is satisfied, α indicates the proportion that is not discharged,and β indicates the incidence of partial discharge.When β = 0,the discharge is extinguished; when β ＜ 1, the reactor is partially discharging; when β = 1, the gas gap is fully bridged.When β = 0 or 1, figure 3(a) is the same as figure 3(b).

Figure 3.Equivalent electrical circuit for PBRs: (a) simplest equivalent circuit; (b) partial-discharge alternative equivalent circuit.

A typical Lissajous figure with a sinusoidal excitation voltage is schematically depicted in figure 4.Due to the periodic change of the applied voltages,the discharge process of the reactor also changes periodically [20].Lines CD and AB correspond to the capacitive phase, and their slopes are equal toCcell.Lines BC and DA correspond to the discharge phase.If the applied voltage is not high enough, the reactor tends to partially discharge and the slopes of lines BC and DA are termed the effective dielectric capacitance ζdiel, which increases with the increase of the applied voltage.If the applied voltage increases to a value far greater than the breakdown voltage,the gas gap will be fully bridged,and ζdielwill be equal toCdiel[16, 18].

For a DBD reactor,the value ofCdielis determined by the dielectric material and the geometric structure.In contrast, in a PBR,each packed particle acts as an individual capacitor of unknown capacitance,andCpackingis also related to the actual packing situation.The value ofCdielof a PBR cannot be easily described by a simple mathematical relationship; it should be determined from Lissajous figures at very high applied voltages[18].The value ofCdielof an empty reactor is equal to the quartz tube capacitanceCqzand can be calculated by equation (1):

wherelis the discharge length(200.0 mm),ε0is the dielectric constant of vacuum (8.85 × 10-12F m−1), εdis the relative dielectric constant of quartz (3.7), andDi(44.0 mm) andDo(50.0 mm) are the inner and outer diameters of the quartz tube, respectively.

In capacitive phase,Cgascan be calculated by equation (2):

The relationship between the effective dielectric capacitance ζdieland other capacitances can be derived using a Lissajous figure and the alternative equivalent circuit depicted in figure 3(b), as given by equation (3).The two coefficients satisfy equation (4).

The values of α and β are defined by equations (5) and(6):

Figure 5.Simplified model of discharge gap in PBR.

For an empty reactor, the equivalent thicknessdgof the gas region is equal to the thickness of the discharge gap.After packing with dielectric particles, a simplified model can be established to determinedg, as shown in figure 5.CgasandCpackingare simplified into two parallel plate capacitors in series.Then,the equivalent thicknessdgof the gas region and the equivalent thicknessdpof the particles region can be calculated by equations (7) and (8).

In equations (7) and (8),Vis the discharge gap volume(52.8 ml),θ is the porosity,dis the outer diameter of the HV electrode (40.0 mm), anddgapis the discharge gap thickness(2.0 mm).

In this work, each piece of measured data was obtained only after the reactor had reached a steady-state.The discharge power was calculated by the Lissajous figure area method, and the slopes were determined by linear fitting.Dielectric particles were tightly packed into the discharge volume,and the relative dielectric constant of glass is about 4.Table 1 presents the equivalent parameters of the reactor.

3.Results and discussion

3.1.Effects of packed particles on partial discharge behavior

3.1.1.Electrical signals and discharge performance.Figure 6 presents the electrical signals of the reactor under four discharge conditions, for which the power was about 100 W.The applied voltage and capacitive current amplitude of the PBR were higher than those of the empty reactor.This phenomenon is related to the particles sharing a portion of the applied voltage.Figure 6(a) presents the typical filamentary discharge of DBD, in which the presence of many messy discharge current pulses is apparent.In comparison, the discharge current pulses are more orderly in figures 6(b)-(d).The packing particles caused a change in the form of discharge; in addition to filamentary discharge, there also existed intensive surface discharge which is beneficial to electron impact ionization and dissociation rates[12,13].The stable microdischarge hold great promise for effective waste gas treatment or ozone synthesis [13].

For a PBR, filaments exist in the voids between the particle-particle/wall,while surface discharge occurs near the contact points between particles.Similar studies have shown that the surface discharge can inhibit nearby filamentary discharge [21].The suppression effect will increase with the decrease of the particle size.By comparing the current signals in figure 6,the particle size effect on the inhibition is evident,while the shape was found to have little effect on the current signal.

As shown in figure 7, the power of the reactor is an increasing function of the applied voltage.Figures 6 and 7 both illustrate that the PBR required a higher applied voltage than the empty reactor to reach the similar power.When the discharge power increased, the heat generated by the reactor also increased.Infrared thermometer was used to irradiate the outer glass tube facing the discharge area.The measured temperature difference is presented in figure 8.With the increase of the applied voltage, the maximum temperature change after stable discharge did not exceed 3.0 °C.This demonstrates that temperature had a limited impact on the dielectric constant of the medium, and it also could help reduce the thermal decomposition of ozone with an oil cooling system [22].

3.1.2.Capacitances from the Lissajous figure.Figure 9 shows the example Lissajous figures for the empty reactor and the PBR with 1.2 mm beads.The shape of the figure changes from a parallelogram to a fusiform when beads were packed in the reactor.The discharge characteristics (e.g.capacitance parameters) have changed.

Figure 10 presents the influence of the packing particles on the cell capacitanceCcelland the effective dielectric capacitance ζd.In the capacitive phase,figure 3(a)is the same as figure 3(b), and the interpretation ofCcellis no different from that of standard theory [15].The value ofCcellof the PBR was significantly higher than that of empty reactor,while the PBRs with different bead sizes had delicate differences between the values ofCcell.

The value of ζdielof the PBR increased almost linearly with the enhanced discharge power,as plotted in figure 10.It can be determined from equation (3) that ζdielis a linear combination ofCcellandCdiel, which is different from the long-standing interpretation.As shown in table 1, the equivalent thicknessdpof the particle region was found to decrease with the increase of the particle size, and the capacitance of the plate capacitor generally increased as the distance between plates decreased.Therefore, the value ofCdielof the PBR increased with the increase of the particle size.The value ofCdielof the empty reactor was larger than that of the PBR.

The increased applied voltage resulted in the increase of the partial discharge coefficient β and the decrease of the nondischarge coefficient α.Consequently, the values of ζdielof the empty reactor and PBR increased and graduallyapproached their respectiveCdielvalues.At high discharge powers, the value’s high-low relationship between ζdielandCdielunder the four discharge conditions exhibited consistency.However, at low discharge powers, only minimal microdischarge occurred, so ζdielwas close toCcell.

Table 1.Discharge gap equivalent parameters of the reactor.

Figure 6.The electrical signals of the reactor at discharge power about 100 W:(a)empty;(b)packed with beads(0.5 mm);(c)packed with beads (1.2 mm); (d) packed with sand (1.0-1.4 mm).

Figure 7.Relationship between the applied voltage and power.

3.1.3.Quantitative evaluation of partial discharge.In a partially discharging PBR system, due to the limited extent of microdischarge over dielectric surface or in void spaces,the non-discharge coefficient α and partial discharge coefficient β can be used to quantify the degree of development of partial discharge, as shown in figure 11.Regardless of whether the reactor was packed or empty,the β curves appear to grow rapidly with the applied voltages.It can also be seen that the α and β curves of the PBR with different bead sizes exhibit a difference at high applied voltages; the PBR with 0.5 mm beads had a larger β value and a lower α value.This reinforces that the degree of partial discharge is dependent on the particle size; the data reveal that a smaller particle size leads to a greater tendency of partial discharge.

Figure 9.Example Lissajous figures for the empty reactor and the PBR with 1.2 mm beads at discharge power about 100 W.

Figure 10.Capacitances extracted from the Lissajous figures at different discharge powers.

Figure 11.Two coefficients at different applied voltages.

Figure 12.Comparison of discharge powers at three β values.

Figure 12 presents the comparison of the discharge power at three β values for four discharge conditions.When the β value was small, the powers were closer.While the increase of the β value to 0.5,the discharge power of the PBR was greater.This may be because the particles led to the expansion of the effective discharge region [13].With the continued increase of the β value, the power difference widened.The PBR with a larger particle size exhibited a better discharge performance.Another explanation is that if the PBRs with different sizes reach similar high discharge powers, the gas gap of the PBR with small beads will be closer to fully-bridged, while that with larger beads will still have room for growth and will retain a certain potential.

3.2.Physical properties derived using partial-discharge alternative equivalent circuit

3.2.1.Variation of Cgasin the capacitive and discharge phase.As the partial discharge coefficient β ＜ 1, a portion of the gas gap capacitance is retained.According to the discharge cycle, the gas gap capacitance can be divided into two phases, namely: the capacitive phaseCgasand the discharge phase αCgas, as depicted in figure 13.Cdielis constant; therefore, the change trend of theCgaswith β is consistent with that ofCcell, i.e.it fluctuates within a certain range.

αCgasis derived from the partial-discharge circuit.During partial discharge, the distinctive feature is that the gas gap microdischarge channels develop rapidly with the increase of the applied voltage,but the entire gas gap has not yet been filled by microdischarge,i.e.Cgasis partially broken down.Consequently, the value of αCgasdecreased significantly but was always greater than zero,as shown in figure 13.When the discharge cycle returned to the capacitive phase,the voltage across the gas gap dropped and α was equal to 1,and the gas gap capacitance returned toCgas.

Figure 13.The gas gap capacitance at different β values.

In addition,it can be seen from figure 13 that in both the discharge and capacitive phases,the values of αCgasandCgascorresponding to PBR were larger than that of the empty reactor.As given in table 1,the equivalent thicknessdgof the gas region of the empty reactor was the largest, and the packing of dielectric particles greatly reduced the value ofdg,thereby significantly increasingCgas.This provides a viable way to avoid fine processing of narrow gaps.The narrow gaps would enhance the density of reactive species or electrons,which is conducive to promoting plasma or O3synthesis[23].

3.2.2.Measured and corrected burning voltages.Theoretically, for any individual void space in which a discharge can occur, positive and negative ions move in the opposite direction under the action of the applied electric field,thereby generating a built-in electric field in the opposite direction.This leads the voltage across microdischarge of the void not change with the applied voltage; rather, it maintains a fixed value, i.e.burning voltage [16, 24].The value of ζdielcan be used to correct the burning voltage obtained from the Lissajous figures during partial discharge, as shown in equation (9), which can be derived from figure 3(b).

whereUbis the corrected burning voltage and ΔUis the measured burning voltage.

Figure 14 presents example burning voltage data for the empty reactor and the PBR with 1.2 mm beads, andUbwas always greater than ΔU.Regarding the changes of ΔUandUbthemselves, ΔUincreased significantly with the increase of β, butUbremained relatively stable, i.e.Ubwas more in line with the preceding theoretical assumption.

From the previous analysis, the gas gap capacitance in the discharge phase exhibited a partial breakdown,this means only local spaces experienced microdischarge.The voltage across these actual individual discharge voids increased to the threshold voltage, but the voltage across the remaining dischargeable space remained below the breakdown threshold.The value of ΔUreflects the overall average of the dischargeable space, so ΔUwas always less thanUb.With the development of the microdischarge,ΔUexhibited a faster growth trend and continued to approachUb.The results indicate that the application of the partial discharge circuit for analysis during partial discharge can help obtain a more accurate burning voltage,while the simplest equivalent circuit will artificially make this value smaller.

Figure 14.Example burning voltage data for the empty reactor and the PBR with 1.2 mm beads at different β values.

Figure 15.The corrected burning voltage at different β values.

Figure 15 presents the corrected burning voltage of PBRs with different bead sizes and an empty reactor.The values ofUbof all reactors increased slightly, but the overall trends were stable;this may be due to higher β values corresponding to higher applied voltages,thereby causing the deeper surface of the original discharge area to participate in microdischarge,or the local electric field strengths to exceed the threshold breakdown strength of individual void spaces [25, 26].Another result revealed in figure 15 is that the values ofUbof PBRs were lower.As reported in similar study, the presence of metal catalyst(Ni/AlO)or dielectric pellets(glass spheres)can decrease the breakdown voltage [21, 27].In the present work, the PBR with 1.2 mm beads had the lowestUbvalue,and decreased bead sizes resulted in increasedUbvalues to some extent.This demonstrates that the complex pore structure in the PBR can effectively reduceUb, weaken the self-sustaining condition of discharge, and increase the likelihood of the occurrence of microdischarge which was beneficial to the generation of plasma active species.The microdischarge in the PBR is a combination of surface discharge and limited filamentary discharge, and the relative contribution of them is related to the particle size [21].Obviously, the combination of microdischarge in the PBR packed with 1.2 mm glass beads seems more reasonable from the perspective of the burning voltage.

Figure 16.The ozone concentration and average applied electric field at different β values.

3.3.Effects of packing particles on the conversion of oxygen to ozone

3.3.1.Particles size/shape factors and ozone concentration.O2passes through the discharge gap,and a portion of this O2is converted to O3.Major reactions for O3synthesis and decomposition are listed as follows [8, 28]:

O3is formed in a three-body reaction,and the surface of the packed particles in PBRs can act as the third body for reaction (12).Moreover, the increased particle surface area promotes reaction (16), and the quenching of O (1D) inhibits reactions (14)-(15), which is beneficial for O3formation.A sufficient number of electrons are needed for the dissociation of O2into O (1D), O (3P).

Figure 17.The ozone concentration and transferred charge per halfcycle at different applied voltages.

Figure 16 reveals that the PBR displayed an obvious advantage in the synthesis of O3as compared with the empty reactor.In a PBR,the presence of contact points between the particle-particle/wall shortens the distance of the independent voids, and the electric field is then distorted.The fact that PBRs can achieve higher electric fields has been confirmed via simulation studies [29, 30].Figure 16 also presents the average electric field as calculated by equation (17).

whereEgis the average electric field of the gas gap andUais the applied voltage.

It is evident that theEgvalues of the PBRs were significantly(about 3-4 times)higher than those of the empty reactor, and corresponding to the high O3concentration.Indeed, the enhancedEgdirectly affected the electron impact dissociation and ionization rates, and more sufficient number of electrons and reactive species was offered, which favored reactions (10)-(13).

Another interesting result conveyed in figure 16 is that the PBR with 0.5 mm beads had the highestEgvalue,but not the highest O3concentration.This demonstrates that O3synthesis is affected by other complex factors [31].Smaller beads correspond to smaller porosity, which results in the increasing pressure of the gas gap and the decrease of the gas density; this further affects the change of the reduced electric field (E/p) [32].Moreover, smaller beads were found to lead to the shorter residence time of O2in the gas gap, which caused a negative effect on O3synthesis[23].In the PBR with 0.5 mm beads, the O2residence time was reduced by nearly 40% as compared to that with 1.2 mm beads.Smaller beads also lead to more local hot spots which can accelerate O3decomposition.These findings indicate that the O3generation ability of the PBR with relatively larger particle sizes was superior under the combined action of multiple factors.

Figure 18.The ozone energy efficiency and production at different discharge powers.

Irregularly-shaped glass sand with a complex surface structure and sizes similar to those of the glass beads was selected for investigation.As plotted in figure 17, the PBR with glass sand also revealed a dependence on particle size in terms of O3synthesis.The curves of the O3concentration of the PBRs with beads (0.5 mm) and sand (0.3-0.6 mm) are relatively close, because the difference in the edge shapes weakened as the size decreased.At high applied voltages,the packing of sand(1.0-1.4 mm)increased the O3concentration by about 6% as compared with the packing of beads (1.2 mm).The plasma voids between irregularly-shaped sandsand/wall were more complicated, containing minor defects,vacancies, edges, corners and so on, all of which would further enhance the collision of O2, reactive species and electrons, which favors O3synthesis.It can be seen from figure 17 that larger-sized particles, as the bridge between electrodes, significantly enhanced the transferred charge per half-cycle, and the packing of sand (1.0-1.4 mm) resulted in slightly increased charge transfer.This provides additional evidence which reflects that a complex surface and irregular pore structure are conducive to the synthesis of plasma activity species.A similar evolution was observed in previous studies, in which changing the pellet shape from spheres to hollow cylinders was found to increase the quantity of the total movement charge in a plasma C2F6removal process [11].

3.3.2.Ozone energy efficiency analysis and comparison.The ozone energy efficiency and production are respectively calculated by equations (18) and (19) as follows:

where η (g·kWh−1) is the ozone energy efficiency, γ (g·h−1)is the ozone production,q(l·min−1)is the flow rate of the feed gas,C(g·m−3) is the ozone concentration, andP(W) is the discharge power.

The relationship between the O3energy efficiency η, O3production γ,and power of the reactor is plotted in figure 18.The η of the empty bed decreased with the increase of the power, while that of the PBR first increased and then continued to decrease.The γ curves are similar to the O3concentration curves; they both increase with the power.It is evident that η and γ are an irreconcilable contradiction, but both can be effectively improved by packing dielectric particles; the energy efficiency and production can be increased by more than 20% and 15%, respectively.

Table 2 shows comparisons with typical parameters of reported in other studies.In a previous work[38],35 parallel glass tubes were used to increase the discharge space and packed aluminum granules were used as the HV electrode;thus, the indicators were higher.A novel geometry with multi-hollow for surface DBD was proposed in [35], O3energy efficiency was greatly improved but O3concentration and production were not outstanding.In this work,the ozone concentration, production, and efficiency were at a more balanced level as compared with those reported in previous research.

It was also found that an excessive particle size increased the difficulty of packing(e.g.the presence of oversized pores,easily getting stuck, and loose packing).Therefore, to optimize the plasma processing capacity for polluted gas or ozone synthesis and avoid the various packing problems, a packing material that has a relatively large size, or that irregularly-shaped and suitable for the discharge gap, is urgently required.

4.Conclusions

The conclusions of this research can be drawn as follows:

(1) The presence of glass particles caused a change in the form of discharge; in addition to filamentary discharge,there also existed surface discharge.Surface discharge can inhibit nearby filamentary discharge, and the suppression effect will be stronger with the decrease of the particle size.

(2) As compared to empty reactor, the values ofCcellandCgasof the PBR were increased,but the value ofCdielof the PBR decreased.As partial discharge,the gas gap of reactor was not fully bridged, and the value of αCgasdecreased with the increase of the value of β, but was greater than zero.This also led the value of ζdielto always be less than the value ofCdiel.

(3) Due to partial discharge, the measured burning voltage ΔUwas artificially smaller than the corrected burning voltageUb.Packed particles can effectively reduce the value ofUband increase the likelihood of the occurrence of discharge.With the decrease of the particle size,Ubwill increase, as will the tendency of partial discharge.

(4) As compared to the empty reactor, the average electric field in the PBR was found to be improved by 3-4 times, and the O3energy efficiency and production were increased by more than 20% and 15%, respectively.The choice of packing materials with relatively large size or irregular shape that is suitable for the discharge gap is therefore beneficial to the improvement of the plasma processing capacity.

Table 2.Comparisons with typical parameters of other reports.

Acknowledgments

This work is currently supported by National Natural Science Foundation of China (Nos.51806085, 51676089), China Postdoctoral Science Foundation (2018M642175), the Double Innovation Talents of Jiangsu Province and Jiangsu University Youth Talent Cultivation Program Funded Project.